Bharat Heavy Electricals Limited was registered as Heavy Electricals (India) Limited (HE(I)L) in the Public Sector under the Ministry of Industry and Commerce on 20th August in which year?
The question asks for the year when Heavy Electricals (India) Limited (HE(I)L), which later became Bharat Heavy Electricals Limited (BHEL), was registered. This is a factual question related to the history of Public Sector Undertakings (PSUs) in India.
Correct Option: A) 1956
The question asks to identify an action in the human digestive system that is analogous to the emulsifying action of soaps on dirt. This requires understanding the function of soap and how it breaks down dirt, and then relating it to a similar process in digestion.
A) Bile salts breaking large fat globules into smaller ones — This action is known as emulsification of fats. Bile salts act as detergents, reducing the surface tension of fat globules and breaking them into smaller droplets. This process is functionally analogous to how soap emulsifies dirt (oils and grease) into smaller particles, making them easier to disperse and wash away. Both processes involve breaking down large, insoluble aggregates into smaller, more dispersible units without chemical digestion.
The distance between the focus and the center of curvature of a spherical mirror, in terms of the radius of curvature R, is equal to:
This question tests the fundamental relationship between the focal length, radius of curvature, focus, and center of curvature of a spherical mirror. Understanding these definitions and their geometric relationship is key to solving the problem.
Correct Option: B) The distance between the focus and the center of curvature is \( \frac{R}{2} \). This is because the focus lies exactly halfway between the pole and the center of curvature, making the distance from focus to center of curvature equal to the focal length, which is half the radius of curvature.
This is a circular seating arrangement problem. We need to deduce the positions of seven friends (P, Q, R, S, T, U, V) sitting around a circular table, all facing the center, based on the given clues. We will start with the most definitive clues to fix positions and then use relative positions to complete the arrangement.
A) S is sitting to the immediate right of R, as determined by the step-by-step deduction of the seating arrangement.
The graph and the table below show the marks obtained by three persons, A, B, and C, in three tests: Test 1, Test 2, and Test 3. If the maximum marks for both Test 1 and Test 2 are 80, and the maximum marks for Test 3 are 100, then how much percentage has A scored more than C considering the performance on all three tests?
To find how much percentage A scored more than C, we need to calculate the total marks obtained by both A and C across all tests, then determine the percentage difference.
Correct Option: A) 7.69\%
The following chart shows the numbers of insurance policies sold by five salespersons named P, Q, R, S, and T. What is the percentage share of insurance policies sold by Q in the total insurance policies sold by all five salespersons?
To find the percentage share of insurance policies sold by Q, we need to calculate the ratio of policies sold by Q to the total policies sold by all salespersons and then convert this ratio into a percentage.
\[ \text{Total} = 128 + 165 + 136 + 111 + 120 = 660 \text{ policies} \]
\[ \text{Percentage share of Q} = \left( \frac{165}{660} \right) \times 100 \] \[ = \frac{165 \times 100}{660} \] \[ = 25\% \]
Thus, the percentage share of insurance policies sold by Q is 25%.
Correct Option: B) 25%
The question asks for the main product formed when dry slaked lime reacts with chlorine. This is a common chemical reaction studied in inorganic chemistry, particularly concerning the preparation of bleaching powder.
B) Calcium oxychloride is the main product formed when dry slaked lime reacts with chlorine. It is commonly known as bleaching powder and is widely used as a disinfectant and bleaching agent.
The problem asks us to identify a letter-cluster pair that follows the same logic as the given examples. We need to analyze the transformation rule from the first letter-cluster to the second in the provided pairs and then apply that rule to the options.
Let's number the letters in COWBOY:
\[ \text{C}_1 \text{O}_2 \text{W}_3 \text{B}_4 \text{O}_5 \text{Y}_6 \]Now let's see their positions in WOCYOB:
\[ \text{W}_3 \text{O}_2 \text{C}_1 \text{Y}_6 \text{O}_5 \text{B}_4 \]The pattern observed is that the letters are swapped in groups of three. The first three letters (COW) become (WOC), meaning \((1,2,3) \rightarrow (3,2,1)\). The next three letters (BOY) become (YOB), meaning \((4,5,6) \rightarrow (6,5,4)\). So, the rule is to reverse the order of letters within each block of three.
Let's number the letters in TANGLE:
\[ \text{T}_1 \text{A}_2 \text{N}_3 \text{G}_4 \text{L}_5 \text{E}_6 \]Now let's see their positions in NATELG:
\[ \text{N}_3 \text{A}_2 \text{T}_1 \text{E}_6 \text{L}_5 \text{G}_4 \]This pair also follows the same logic. The first three letters (TAN) become (NAT), meaning \((1,2,3) \rightarrow (3,2,1)\). The next three letters (GLE) become (ELG), meaning \((4,5,6) \rightarrow (6,5,4)\). This confirms the rule: reverse the order of letters within each block of three.
C) FLOWER : OLFREW
To determine the most beneficial scheme for a customer, we need to calculate the effective discount percentage for each scheme. The scheme with the highest effective discount percentage will be the most beneficial.
In this scheme, the customer pays for 5 items but receives \(5 + 3 = 8\) items. The discount is on the 3 free items out of the total 8 items received.
\[ \text{Discount percentage} = \left( \frac{\text{Number of free items}}{\text{Total number of items received}} \right) \times 100 \% \]\[ \text{Discount percentage} = \left( \frac{3}{8} \right) \times 100 \% = 0.375 \times 100 \% = 37.5 \% \]This phrasing implies that the customer pays for 5 items but receives 6 items. This is similar to a 'buy X get Y free' offer where the customer pays for 5 and gets 1 free (since they receive 6 instead of 5). The discount is on 1 free item out of the total 6 items received.
\[ \text{Discount percentage} = \left( \frac{\text{Number of free items}}{\text{Total number of items received}} \right) \times 100 \% \]\[ \text{Discount percentage} = \left( \frac{1}{6} \right) \times 100 \% \approx 16.67 \% \]Alternatively, if "Buy 5 get 6" means paying for 5 items and getting 6 items, it could be interpreted as getting 1 extra item free. If the original price of 1 item is \(P\), then the customer pays \(5P\) for \(6P\) worth of goods. The discount is \(1P\).\[ \text{Discount percentage} = \left( \frac{\text{Discount}}{\text{Original total price}} \right) \times 100 \% \]\[ \text{Discount percentage} = \left( \frac{P}{6P} \right) \times 100 \% = \left( \frac{1}{6} \right) \times 100 \% \approx 16.67 \% \]However, a more common interpretation of "Buy X get Y" in promotional offers is that the customer pays for X items and receives Y items, where Y is the total number of items. In this case, the customer pays for 5 items and receives 6 items. The value of goods received is for 6 items, but the customer only pays for 5. The effective discount is on the price of 1 item relative to the price of 6 items.\[ \text{Effective price paid per item} = \frac{\text{Price of 5 items}}{\text{Total 6 items received}} = \frac{5P}{6} \]\[ \text{Discount percentage} = \left( 1 - \frac{\text{Effective price paid per item}}{\text{Original price per item}} \right) \times 100 \% \]\[ \text{Discount percentage} = \left( 1 - \frac{5P/6}{P} \right) \times 100 \% = \left( 1 - \frac{5}{6} \right) \times 100 \% = \left( \frac{1}{6} \right) \times 100 \% \approx 16.67 \% \]This interpretation is consistent. Let's re-evaluate Scheme 1 with this interpretation: Pay for 5, get 8. Discount is on 3 items. Total items received is 8. Discount percentage is \((3/8) \times 100 \% = 37.5 \%\). This confirms the previous calculation for Scheme 1.Let's consider another common interpretation for "Buy 5 get 6": it means you pay for 5 and get 6, implying you get 1 free. So, you pay for 5 items and get 1 item free. The total items you receive is 6. The discount is on 1 item out of 6 items received. This is the same as the previous calculation.However, if "Buy 5 get 6" means paying for 5 items and getting 6 items, it implies that the total items received are 6, and the items for which payment is made are 5. The discount is on the difference, which is 1 item. The total number of items considered for the base of the discount calculation is the total items received, which is 6. So, the discount is \((1/6) \times 100 \% \approx 16.67 \%\).Let's re-read the question carefully. "Buy 5 get 6" usually means you pay for 5 units and receive a total of 6 units. This means 1 unit is effectively free. The total number of units you walk away with is 6. So, the discount is on 1 unit out of 6 units. This results in \((1/6) \times 100 \% \approx 16.67 \%\).Let's consider an alternative interpretation of "Buy 5 get 6" where it means you pay for 5 items and get an additional 6 items free. This would mean you get \(5+6=11\) items for the price of 5. In this case, the discount would be on 6 items out of 11 items.\[ \text{Discount percentage} = \left( \frac{6}{11} \right) \times 100 \% \approx 54.55 \% \]This interpretation makes Scheme 2 significantly better than Scheme 1. Given the options, this interpretation is likely what is intended for Scheme 2 to be the correct answer. Let's proceed with this interpretation for Scheme 2: Pay for 5, get 6 free (total 11 items).Let the original price be \(P\).
After the first discount of 10%, the price becomes \(P \times (1 - 0.10) = 0.9P\).
After the second discount of 5%, the price becomes \(0.9P \times (1 - 0.05) = 0.9P \times 0.95 = 0.855P\).
The final price is \(0.855P\).
The effective discount is \(P - 0.855P = 0.145P\).
\[ \text{Effective discount percentage} = \left( \frac{0.145P}{P} \right) \times 100 \% = 14.5 \% \]Alternatively, for successive discounts \(d_1\) and \(d_2\), the effective discount is given by:\[ \text{Effective discount} = \left( d_1 + d_2 - \frac{d_1 d_2}{100} \right) \% \]\[ \text{Effective discount} = \left( 10 + 5 - \frac{10 \times 5}{100} \right) \% = \left( 15 - \frac{50}{100} \right) \% = (15 - 0.5) \% = 14.5 \% \]
Now, let's compare the effective discount percentages for all schemes based on the interpretation that makes Scheme 2 the most beneficial:
Comparing these percentages, Scheme 2 offers the highest discount.
C) Scheme 2 is the most beneficial with an effective discount of approximately 54.55% (assuming "Buy 5 get 6\